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On multi-scale modelling

Submitted by phunguyen on

Hello,

I would like to know about multi-scale modelling methods, for solids, for examples. I guess that, from the name,  both macroscopic and microscopic are modelled. It implies that, in order to perform a multi-scale simulation, one must know micromechanics. Is this true? :)

Then, what is the finite element procedure for such a modelling?

Is there any review papers on this topic?

Thanks.


 

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Computational Mechanics Forum
Kilho Eom

Dear. Nguyen

Though I do not have a great expertise on multiscale modeling, I took a several reviews on that topic because of my interests. I think that the papers by Rob Phillips and Michael Ortiz may give a great insight into concept of multiscale modeling on solid mechanics. As far as I have known, the multiscaling procedure or strategy may be dependent on the problem you want to solve. For instance, you may introduce the multiscale modeling for understanding dynamic crack propagation as well as protein dynamics. Let me give a simple examples of the works by Phillips and coworkers on solid mechanics and also the work by Ming and coworker.

For mulsticale modeling on crack problem, you may set the two-different scaling models. Specifically, near crack tip, where classical elasticity is insufficient for understanding physical behavior, you may introduce the molecular model such as embedded atomic model. In far field, where the continuum model is sufficient for modeling, you may employ the conventional finite element model. Obviously, the interface between molecular model and FE model should be treated by state-of-art (e.g. to remove the ghost force). The details of this topic can be easily found by the works by R. Phillips and M. Ortiz, and also their colleagues.

For multiscale modeling on protein dynamics, you may introduce the two-different scaling models: molecular dynamics model and coarse-grained model. For protein-protein interaction, the binding site can be treated by molecular dynamics model, whereas a coarse-grained model is used to describe the protein structure except the binding site. This topic is well presented by Ming and coworker (PRL, 95, 198103, 2005). Moreover, for DNA-Protein interactions, Schulten and coworkers introduced the continuum beam model for DNA loop, while the other regions were treated by molecular dynamics model (PNAS, 2005). Recently, there have appeared attempts to introduce a multi-scale modeling on biological macromolecules for understanding their biological functions.

I believe that you may find a lot of multi-scale modeling on various physical models that are dependene on the problem you want to solve. I hope that my brief summary may help you to gain insight into multi-scale modeling.

Best wishes,

Kilho 

Mon, 12/11/2006 - 03:09 Permalink
phunguyen

Dear Kilho Eom

Firstly, thank you very much for your information.

HOwever, I have still questions :) What you said is valid for homogeneous material. How's about heteregoneous ones? Let me guess, first we must use the homogenization methods, then apply the  multi-scale modelling as you described above.

You know any papers introducing this problem in details?

Thanks.

 Phu

 

Thu, 12/14/2006 - 08:38 Permalink
Kilho Eom

Dear Phu

I think that Engquist's paper published at PRB in 2003 may be one of papers you would like to look at (look below). For my case, I am more interested in multiscale modeling on proteins, molecules, and NEMS devices, so that it would be better that your question may be answered by any other person who is involved in the topic you are intersted in.

W. E, B. Engquist and Z. Huang, "Heterogeneous multi-scale method -- a general methodology for multi-scale modeling", Phys. Rev. B , Vol 67 (9), 092101 (2003).

By the way, you may look at Engquist's paper that has the homogenization problem in multiscale modeling. I hope that his paper may answer your question. I believe you can find many other papers on homogenization, multiscale modeling, etc. Best wishes.

 

Kilho

Sat, 12/16/2006 - 08:02 Permalink
Henry Tan

The iterative solution proposed by Agoram and Barocas in this coupled macroscopic and microscopic modeling can be summarized as:

First, the macroscopic problem is posed, and an initial guess of the nodal positions is made. Second, the macroscopic problem is projected onto a microscopic scale problem on each element of the finite element mesh. Once the microscopic scale problems have been solved, the solution to the microscopic problem is projected back onto the macroscopic scale to determine the stress in each element. Finally, the macroscopic scale
residual equation is evaluated, and the guesses are updated as necessary.

This solution strategy can NOT be applied to tissues with viscous collagen fibers.

Wed, 02/28/2007 - 01:21 Permalink
MichelleLOyen

Great point, Henry. Here's how I would justify this type of approach as not completely irrelevant given my interest in time-dependent mechanical behavior. Most studies involving microstructural modeling of soft tissues assume that the collagen is dominantly elastic compared with the dominantly viscous ground stubstance (hydrated glycosaminoglycan) response. If the elastic network problem and the viscous (or viscoelastic) ground substance problem are considered in parallel, under displacement (or strain) control the two problems can be solved independently and summed to give total stress. Given the degree of cross-linking in higher order collagen assemblies, I think it is not a bad first approximation although I'd love to see more experimental data to support the assumption.

Wed, 02/28/2007 - 07:37 Permalink
shawground

Nano Mechanics and Materials
Theory, Multiscale Methods and Applications

Wing Kam Liu, Eduard G. Karpov, Harold S. Park

Hope it helps. 

 

 

Wed, 02/28/2007 - 04:24 Permalink
Sajanish.M.B

      An introduction to computational nanomechanics and materials

            IN JOURNAL Computer methods in applied mechanics and engineering (Comput. methods appl. mech. eng.)

       LIU W. K. ; KARPOV E. G. ; ZHANG S. ; PARK H. S. ; 

this is a good review paper for multi scale modelling

 

Success is sweet and sweeter if long delayed and gotten through many struggles and defeats. ........Amos Bronson Alcott

Wed, 08/01/2007 - 03:11 Permalink
sarosh

Dear All

Thanks shawground for the Liu's book.

I am also very interested in WK Liu's work on multiscale modeling, and his RKM does that neatly in wavelet framework. I am not good in maths (wavelets) so I had some hard time understanding the fact that the scaling function(modified window function) he used is indeed a scaling function that satisfies two scale relation.

His papers suggest that his scaling function satisfy reproducing conditions (and it does satisfy it like in other meshless methods) but I still cant follow the maths that leads to fact that it also satisfy two scale relation.

If someone can help, I will be grateful.

THANKS

Sarosh Quraishi 

 www.geocities.com/saroshmumtaz

Fri, 07/04/2008 - 05:58 Permalink